A017455 -id:A017455 - cp's OEIS frontend

A017449 a(n) = 11*n + 5.

5, 16, 27, 38, 49, 60, 71, 82, 93, 104, 115, 126, 137, 148, 159, 170, 181, 192, 203, 214, 225, 236, 247, 258, 269, 280, 291, 302, 313, 324, 335, 346, 357, 368, 379, 390, 401, 412, 423, 434, 445, 456, 467, 478, 489, 500, 511, 522, 533, 544, 555, 566, 577, 588

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A008593, A017401, A017437.

Powers of the form (11*n+5)^m: this sequence (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..60], n-> 11*n+5); # G. C. Greubel, Sep 18 2019

[11*n+5: n in [0..60]]; // Vincenzo Librandi, Sep 03 2011

seq(11*n+5, n=0..60); # G. C. Greubel, Sep 18 2019

Range[5, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
LinearRecurrence[{2,-1},{5,16},60] (* Harvey P. Dale, Apr 15 2019 *)

a(n)=11*n+5 \\ Charles R Greathouse IV, Jul 10 2016

[11*n+5 for n in (0..60)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: (5 + 6*x)/(1-x)^2.
E.g.f.: (5 + 11*x)*exp(x). (End)

A017450 a(n) = (11*n + 5)^2.

Original entry on oeis.org

25, 256, 729, 1444, 2401, 3600, 5041, 6724, 8649, 10816, 13225, 15876, 18769, 21904, 25281, 28900, 32761, 36864, 41209, 45796, 50625, 55696, 61009, 66564, 72361, 78400, 84681, 91204, 97969, 104976, 112225, 119716, 127449, 135424, 143641, 152100, 160801, 169744, 178929, 188356, 198025

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Powers of the form (11*n+5)^m: A017449 (m=1), this sequence (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..45], n-> (11*n+5)^2); # G. C. Greubel, Sep 18 2019

[(11*n+5)^2: n in [0..45]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^2, n=0..45); # G. C. Greubel, Sep 18 2019

(11Range[0,45]+5)^2 (* or *) LinearRecurrence[{3,-3,1},{25,256,729},45] (* Harvey P. Dale, Dec 08 2013 *)

a(n)=(11*n+5)^2 \\ Charles R Greathouse IV, Jun 17 2017

[(11*n+5)^2 for n in (0..45)] # G. C. Greubel, Sep 18 2019

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=25, a(1)=256, a(2)=729. - Harvey P. Dale, Dec 08 2013
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (25 +181*x +36*x^2)/(1-x)^3.
E.g.f.: (25 +231*x +121*x^2)*exp(x). (End)

A017451 a(n) = (11*n + 5)^3.

Original entry on oeis.org

125, 4096, 19683, 54872, 117649, 216000, 357911, 551368, 804357, 1124864, 1520875, 2000376, 2571353, 3241792, 4019679, 4913000, 5929741, 7077888, 8365427, 9800344, 11390625, 13144256, 15069223, 17173512, 19465109, 21952000, 24642171, 27543608, 30664297, 34012224, 37595375, 41421736

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), this sequence (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..40], n-> (11*n+5)^3); # G. C. Greubel, Sep 18 2019

[(11*n+5)^3: n in [0..40]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^3, n=0..40); # G. C. Greubel, Sep 18 2019

(11*Range[40] -6)^3 (* G. C. Greubel, Sep 18 2019 *)

vector(40, n, (11*n-6)^3) \\ G. C. Greubel, Sep 18 2019

[(11*n+5)^3 for n in (0..40)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (125 +3596*x +4049*x^2 +216*x^3)/(1-x)^4.
E.g.f.: (125 +3971*x +5808*x^2 +1331*x^3)*exp(x). (End)

A017452 a(n) = (11*n + 5)^4.

Original entry on oeis.org

625, 65536, 531441, 2085136, 5764801, 12960000, 25411681, 45212176, 74805201, 116985856, 174900625, 252047376, 352275361, 479785216, 639128961, 835210000, 1073283121, 1358954496, 1698181681, 2097273616, 2562890625, 3102044416, 3722098081, 4430766096, 5236114321, 6146560000

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), this sequence (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..30], n-> (11*n+5)^4); # G. C. Greubel, Sep 18 2019

[(11*n+5)^4: n in [0..30]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^4, n=0..30); # G. C. Greubel, Sep 18 2019

(11*Range[30] -6)^3 (* G. C. Greubel, Sep 18 2019 *)
LinearRecurrence[{5,-10,10,-5,1},{625,65536,531441,2085136,5764801},30] (* Harvey P. Dale, Nov 29 2022 *)

vector(30, n, (11*n-6)^4) \\ G. C. Greubel, Sep 18 2019

[(11*n+5)^4 for n in (0..30)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (625 +62411*x +210011*x^2 +77041*x^3 +1296*x^4)/(1-x)^5.
E.g.f.: (625 +64911*x +200497*x^2 +114466*x^3 +14641*x^4)*exp(x). (End)

A017453 a(n) = (11*n + 5)^5.

Original entry on oeis.org

3125, 1048576, 14348907, 79235168, 282475249, 777600000, 1804229351, 3707398432, 6956883693, 12166529024, 20113571875, 31757969376, 48261724457, 71008211968, 101621504799, 141985700000, 194264244901

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), this sequence (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..30], n-> (11*n+5)^5); # G. C. Greubel, Sep 18 2019

[(11*n+5)^5: n in [0..30]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^5, n=0..30); # G. C. Greubel, Sep 18 2019

(11*Range[31] -6)^5 (* G. C. Greubel, Sep 18 2019 *)

vector(30, n, (11*n-6)^5) \\ G. C. Greubel, Sep 18 2019

[(11*n+5)^5 for n in (0..30)] # G. C. Greubel, Sep 18 2019

From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (3125 +1029826*x +8104326*x^2 +8807866*x^3 +1373201*x^4 +7776*x^5)/(1-x)^6.
E.g.f.: (3125 +1045451*x +6127440*x^2 +6555175*x^3 +1976535*x^4 +161051*x^5)*exp(x). (End)

A017454 a(n) = (11*n + 5)^6.

Original entry on oeis.org

15625, 16777216, 387420489, 3010936384, 13841287201, 46656000000, 128100283921, 304006671424, 646990183449, 1265319018496, 2313060765625, 4001504141376, 6611856250609, 10509215371264, 16157819263041, 24137569000000, 35161828327081, 50096498540544, 69980368892329

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), this sequence (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..20], n-> (11*n+5)^6); # G. C. Greubel, Sep 18 2019

[(11*n+5)^6: n in [0..20]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^6, n=0..20); # G. C. Greubel, Sep 18 2019

(11*Range[0,30]+5)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {15625, 16777216, 387420489, 3010936384, 13841287201, 46656000000, 128100283921}, 30] (* Harvey P. Dale, Dec 12 2013 *)

vector(20, n, (11*n-6)^6) \\ G. C. Greubel, Sep 18 2019

[(11*n+5)^6 for n in (0..20)] # G. C. Greubel, Sep 18 2019

a(n) = 7*a(n-1) -21*a(n-2) +35*a(n-3) -35*a(n-4) +21*a(n-5) -7*a(n-6) + a(n-7); a(0)=15625, a(1)=16777216, a(2)=387420489, a(3)=3010936384, a(4)=13841287201, a(5)=46656000000, a(6)=128100283921. - Harvey P. Dale, Dec 12 2013
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: (15625 +16667841*x +270308102*x^2 +650767622*x^3 +313907097*x^4 +23810977*x^5 +46656*x^6)/(1-x)^7.
E.g.f.: (15625 +16761591*x +176940841*x^2 +316498490*x^3 +168957140*x^4 +31404945*x^5 +1771561*x^6)*exp(x). (End)

A017456 a(n) = (11*n + 5)^8.

Original entry on oeis.org

390625, 4294967296, 282429536481, 4347792138496, 33232930569601, 167961600000000, 645753531245761, 2044140858654976, 5595818096650401, 13685690504052736, 30590228625390625, 63527879748485376, 124097929967680321, 230193853492166656, 408485828788939521

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), this sequence (m=8), A017457 (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..20], n-> (11*n+5)^8); # G. C. Greubel, Sep 19 2019

[(11*n+5)^8: n in [0..20]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^8, n=0..20); # G. C. Greubel, Sep 19 2019

(11Range[0,20]+5)^8  (* Harvey P. Dale, Apr 23 2011 *)

vector(20, n, (11*n-6)^8) \\ G. C. Greubel, Sep 19 2019

[(11*n+5)^8 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (390625 +4291451671*x +243788893317*x^2 +1960512320323*x^3 +3909536602339*x^4 +2202777455589*x^5 +315080647543*x^6 +6960640897*x^7 +1679616*x^8)/(1-x)^9.
E.g.f.: (390625 +4294576671*x +136919996257*x^2 +585564673386*x^3 +729964989831*x^4 +353933730150*x^5 +74628778686*x^6 +6781535508*x^7 + 214358881*x^8)*exp(x). (End)

A017457 a(n) = (11*n + 5)^9.

Original entry on oeis.org

1953125, 68719476736, 7625597484987, 165216101262848, 1628413597910449, 10077696000000000, 45848500718449031, 167619550409708032, 520411082988487293, 1423311812421484544, 3517876291919921875

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), this sequence (m=9), A017458 (m=10), A017459 (m=11), A017460 (m=12).

List([0..20], n-> (11*n+5)^9); # G. C. Greubel, Sep 19 2019

[(11*n+5)^9: n in [0..20]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^9, n=0..20); # G. C. Greubel, Sep 19 2019

(11Range[0,20]+5)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210, 120,-45,10,-1}, {1953125, 68719476736, 7625597484987, 165216101262848, 1628413597910449, 10077696000000000, 45848500718449031, 167619550409708032, 520411082988487293, 1423311812421484544}, 20] (* Harvey P. Dale, Apr 08 2019 *)

vector(20, n, (11*n-6)^9) \\ G. C. Greubel, Sep 19 2019

[(11*n+5)^9 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (1953125 +68699945486*x +6938490608252*x^2 +92052268491098*x^3 +311158545054314*x^4 +327643477452290*x^5 +108279046743524*x^6 +9393030684758*x^7 +118487099537*x^8 +10077696*x^9)/(1-x)^10.
E.g.f.: (1953125 +68717523611*x +3744080242320*x^2 +23757577547495*x^3 +42209495908965*x^4 +29265638697141*x^5 +9191914318356*x^6 +1377002477202*x^7 +94532266521*x^8 +2357947691*x^9)*exp(x). (End)

A017458 a(n) = (11*n + 5)^10.

Original entry on oeis.org

9765625, 1099511627776, 205891132094649, 6278211847988224, 79792266297612001, 604661760000000000, 3255243551009881201, 13744803133596058624, 48398230717929318249, 148024428491834392576

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), this sequence (m=10), A017459 (m=11), A017460 (m=12).

List([0..20], n-> (11*n+5)^10); # G. C. Greubel, Sep 19 2019

[(11*n+5)^10: n in [0..10]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^10, n=0..20); # G. C. Greubel, Sep 19 2019

(11*Range[21] -6)^10 (* G. C. Greubel, Sep 19 2019 *)
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{9765625,1099511627776,205891132094649,6278211847988224,79792266297612001,604661760000000000,3255243551009881201,13744803133596058624,48398230717929318249,148024428491834392576,404555773570791015625},20] (* Harvey P. Dale, Aug 19 2020 *)

vector(20, n, (11*n-6)^10) \\ G. C. Greubel, Sep 19 2019

[(11*n+5)^10 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (9765625 +1099404205901*x +193797041298488*x^2 +4073880923146640* x^3 +21874532039020442*x^4 +38639279895450554*x^5 +24069986191404704*x^6 +4993111339147592*x^7 +274024159430165*x^8 +2015328772513*x^9 +60466176* x^10)/(1-x)^11.
E.g.f.: (9765625 +1099501862151*x +101846059302361*x^2 +943972829470330* x^3 +2329598652561730*x^4 +2220242776827075*x^5 +974547942271827*x^6 + 214025260632480*x^7 +23938528035675*x^8 +1285081491595*x^9 +25937424601* x^10)*exp(x). (End)

A017459 a(n) = (11*n + 5)^11.

Original entry on oeis.org

48828125, 17592186044416, 5559060566555523, 238572050223552512, 3909821048582988049, 36279705600000000000, 231122292121701565271, 1127073856954876807168, 4501035456767426597157, 15394540563150776827904

Offset: 0

N. J. A. Sloane

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).

Powers of the form (11*n+5)^m: A017449 (m=1), A017450 (m=2), A017451 (m=3), A017452 (m=4), A017453 (m=5), A017454 (m=6), A017455 (m=7), A017456 (m=8), A017457 (m=9), A017458 (m=10), this sequence (m=11), A017460 (m=12).

List([0..20], n-> (11*n+5)^11); # G. C. Greubel, Sep 19 2019

[(11*n+5)^11: n in [0..10]]; // Vincenzo Librandi, Sep 03 2011

seq((11*n+5)^11, n=0..20); # G. C. Greubel, Sep 19 2019

(11Range[0,20]+5)^11 (* Harvey P. Dale, May 12 2011 *)

vector(20, n, (11*n-6)^11) \\ G. C. Greubel, Sep 19 2019

[(11*n+5)^11 for n in (0..20)] # G. C. Greubel, Sep 19 2019

From G. C. Greubel, Sep 19 2019: (Start)
G.f.: (48828125 +17591600106916*x +5347957556678781*x^2 + 173024396961630192*x^3 +1409984186533172778*x^4 +3893323100536505064*x^5 +4065965093212217778*x^6 +1612934439380337744*x^7 +220215589053761433* x^8 +7882270656385972*x^9 +34267542742961*x^10 +362797056*x^11)/(1-x)^12.
E.g.f.: (48828125 +17592137216291*x +2761938121647408*x^2 + 36991274172198511*x^3 +124534035099698400*x^4 +158840151787803530*x^5 + 93615574446397542*x^6 +28270098736853457*x^7 +4580560974275055*x^8 + 396972283518305*x^9 +17118700236660*x^10 +285311670611*x^11)*exp(x). (End)

cp's OEIS Frontend

A017449 a(n) = 11*n + 5.

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A017450 a(n) = (11*n + 5)^2.

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A017451 a(n) = (11*n + 5)^3.

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A017452 a(n) = (11*n + 5)^4.

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A017453 a(n) = (11*n + 5)^5.

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A017454 a(n) = (11*n + 5)^6.

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Magma